New post in Ring-theory

Show that $\Bbb R[x]/\langle x^{2}+1\rangle$ is a field.

August 18th, 2022

Is the set of all 2x2 matrices a ring with zero divisors?

August 15th, 2022

Structure theorem of Artinian rings

November 7th, 2022

Describe all extensions of the identity map of $\mathbb{Q}$ to an isomorphism mapping $\mathbb{Q}(\sqrt[3]{2},\sqrt{3})$

April 9th, 2020

If R is an integral domain disprove the RxR is an integral domain?

December 19th, 2020

Let $M$ be a maximal ideal of a ring $R$. Is $M[x]$ a maximal ideal of $R[x]$?

August 1st, 2022

Gaussian integers modulo n. Multiplication table for $\mathbb Z_3[i]$.

August 1st, 2022

Prove that R is a field ↔ The only ideals in R are R(0) and (0).

January 23rd, 2020

Finite integral domain

February 4th, 2020

Every maximal ideal is a prime ideal

September 7th, 2020

Show that $\mathbb{Z}_n$ is local ring iff $n$ is a power of a prime number

August 1st, 2022

The quotient ring $\mathbb{Z}[i]/(1 + i)$

June 5th, 2020

Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.

August 1st, 2022

Prove that if $R$ is a principal ideal ring and $S$ is a multiplicatively closed subset of $R$ then $S^{-1}R$ is also a principal ideal ring.

August 1st, 2022

Definition of residue in context of the polynomial ring of $\mathbb{Z}[x]/(f)$?

February 10th, 2022

Understanding the quotient ring $\mathbb{Q}[x]/x^2$ up to isomorphism

August 1st, 2022

How to factor polynomials into irreducible factors in a particular ring?

August 1st, 2022

Proving that End(V) is isomorphic to a matrix ring

August 1st, 2022

Subfield of a field F

August 1st, 2022

Ring of Fractions Isomorphic to Subring of Quotient Field.

July 18th, 2020

Give an example to show that a factor ring of an integral domain may be a field

August 1st, 2022

How to check if a function is an homomorphism?

August 1st, 2022

Prove a Field is a commutative ring with identity

August 1st, 2022

Find ring homorphisms from $\Bbb Z_2$ to $\Bbb Z_6$

August 1st, 2022

Solve the equation $3x=2$ in the fields $\mathbb Z_7$ and $\mathbb Z_{23}$

October 11th, 2020

Prove $R \times R$ is NOT an integral domain

August 1st, 2022

Finitely generated ring.

August 1st, 2022

Noetherian group rings

August 1st, 2022

Left ideals of matrix rings are direct sum of column spaces?

November 18th, 2020

Matrix rings and ideals

November 25th, 2020